Hi, there! I'm happy to help with this.

This is a deep conceptual question. I would say: think about translating from the situation into pure math terms.

Essentially, we are being asked: does m divide evenly in n? If m divides evenly into n, then the quotient n/m will be the exact number of students in each classroom. If m doesn't divide evenly into n, then when we divide, we will get a remainder, and when we put those "remainder" kids into the m classrooms, that will make some of the rooms have more students than others.

Statement #1 says that 3n is evenly divisible by m --- i.e. the quotient (3n)/m has no remainder. This could happen if n/m to begin with --- say n = 56 and m = 7 --- if m goes into n, it will go into 3n. Or, it could happen if m is divisible by 3 and another factor, and n is divisible only by this second factor --- for example, if m = 6 and n = 22, then m goes evenly into 3n = 66, but not into n. Because there are two cases, there's no way to decide whether m divides evenly into n. Statement #1 is not sufficient.

Statement #1 says that 13n is evenly divisible by m --- i.e. the quotient (13n)/m has no remainder. Here, there's no way that m has a factor of 13 in it, because we are told m < 13. Any factor of m greater than one will not divide into 13, because 13 is prime. Therefore, the only way m will divide evenly into 13n is if it divides evenly into n. This unambiguously answers the question. Therefore, Statement #2 is sufficient.

Answer = B

Does that make sense? Let me know if you have any questions.

Here's another problem about numbers & factors, just for practice:

https://gmat.magoosh.com/questions/308

Mike

kishokbabu wrote:A school administrator will assign each student in
a group of n students to one of m classrooms. If
3 < m < 13 < n, is it possible to assign each of the
n students to one of the m classrooms so that each
classroom has the same number of students assigned
to it?

(1) It is possible to assign each of 3n students to
one of m classrooms so that each classroom
has the same number of students assigned to it.

(2) It is possible to assign each of 13n students to
one of m classrooms so that each classroom
has the same number of students assigned to it.

The question can be rephrased as "If 3 < m < 13 < n, is n/m an integer?"

(1) The information in statement 1 implies that 3n/m is an integer. Now we have find whether n/m is an integer.
Given that 3 < m < 13 < n, if n = 36 and m = 6, then n/m is an integer.
On the other hand if n = 40 and m = 6, then n/m is not an integer.
Since we don't get a unique answer, so (1) is NOT SUFFICIENT.

(2) According to the statement, 13n/m is an integer.
3 < m < 13 < n implies that m lies between 3 and 13 but is not 13, so 13n/m can be integer only if n/m is an integer.
So, (2) is SUFFICIENT.

The correct answer is B.